\Header{PP.test}{Phillips-Perron Test for Unit Roots}
\keyword{ts}{PP.test}
\begin{Description}\relax
Computes the Phillips-Perron test for the null hypothesis that
\code{x} has a unit root against a stationary alternative.\end{Description}
\begin{Usage}
\begin{verbatim}
PP.test(x, lshort = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a numeric vector or univariate time series.
\item[\code{lshort}] a logical indicating whether the short or long version
of the truncation lag parameter is used.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The general regression equation which incorporates a constant and a
linear trend is used and the corrected t-statistic for a first order
autoregressive coefficient equals one is computed.  To estimate
\code{sigma\textasciicircum{}2} the Newey-West estimator is used.  If \code{lshort}
is \code{TRUE}, then the truncation lag parameter is set to
\code{trunc(4*(n/100)\textasciicircum{}0.25)}, otherwise
\code{trunc(12*(n/100)\textasciicircum{}0.25)} is used.  The \eqn{p}{}-values are
interpolated from Table 4.2, page 103 of Banerjee \emph{et al.}
(1993).

Missing values are not handled.\end{Details}
\begin{Value}
A list with class \code{"htest"} containing the following components:
\begin{ldescription}
\item[\code{statistic}] the value of the test statistic.
\item[\code{parameter}] the truncation lag parameter.
\item[\code{p.value}] the \eqn{p}{}-value of the test.
\item[\code{method}] a character string indicating what type of test was
performed.
\item[\code{data.name}] a character string giving the name of the data.
\end{ldescription}
\end{Value}
\begin{Author}\relax
A. Trapletti\end{Author}
\begin{References}\relax
A. Banerjee, J. J. Dolado, J. W. Galbraith, and D. F. Hendry (1993)
\emph{Cointegration, Error Correction, and the Econometric Analysis
of Non-Stationary Data}, Oxford University Press, Oxford.

P. Perron (1988) Trends and random walks in macroeconomic time
series. \emph{Journal of Economic Dynamics and Control} \bold{12},
297--332.\end{References}
\begin{Examples}
\begin{ExampleCode}
x <- rnorm(1000)
PP.test(x)
y <- cumsum(x) # has unit root
PP.test(y)
\end{ExampleCode}
\end{Examples}

